EDIT: I just realized you were talking 1 degree on the heat side, just ignore this post.
Sensor is in a thermowell, so I'll set both sides to 68 with 1 degree differential. Thanks zorch
I don't have a Ranco so this advice might not be worth a crap, but when I set mine to 1 degree it would occasionally cycle the freezer for about a second then shut it off. The temp reading would sometimes flip back and forth from, say, 67 to 68 then back to 67 as it was warming up. I switched to a 2 degree swing and it solved than problem. When I set to 67 it will go down to 67.9 then up to 69.0 then back down, effectively 68. Stupid but it works.
I have this controller: http://www.amazon.com/gp/product/B0057APQIY/ref=oh_o04_s00_i00_details
Anyway, just thought I would chime in just in case.